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The electroelastic problem of the stress state of an electroelastic transversely isotropic medium in which a rigid disk-shaped inclusion is displaced under a load non-centrally applied to its surface is solved exactly. Closed analytical expressions for displacements and stress distributions in the piezoelectric material below the inclusion are derived. The solutions of the static electroelastic equations for a transversely isotropic body represented in terms of harmonic functions are used. The problem is reduced to pair integral equations. Expressions for the stress state of a purely elastic transversely isotropic material with a disk-shaped inclusion under non-central load on its surface the follow from the obtained analytical formulas as partial cases. The effect of the coupling of the mechanical and electric fields on the stress distribution below the rigid inclusion under non-central loading is studied numerically. [ABSTRACT FROM AUTHOR]

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The problem of the stress state in an orthotropic piezoelectric body with a triaxial ellipsoidal inclusion under homogeneous force and electric loads is considered. The problem is solved by the Eshelby method of equivalent inclusion generalized to the case of a piezoelectric orthotropic space. The approach is validated against the example of a spheroidal cavity in a transversely isotropic material (the axis of revolution coincides with the symmetry axis) for which the exact solution is known. The stress distribution over the surface of the ellipsoidal cavity subject to tension is analyzed numerically. [ABSTRACT FROM AUTHOR]

The paper gives explicit expressions of the elastic T-stress components T I, T II, and T III for an elliptic crack in an unbounded body under uniform pressure and bending and expressions of all the T-stress components for parabolic and tunnel cracks under uniform loading. These formulas are derived by analyzing the asymptotic behavior of the stress components near the crack front using special harmonic functions. The dependence of the T-stresses on Poisson’s ratio, semiaxes and parametric angle of the elliptic crack is studied. The expressions of T I, T II, and T III for a penny-shaped crack under arbitrary uniform pressure and bending follow as a special case from the respective expressions for an elliptic crack [ABSTRACT FROM AUTHOR]

The stress state of an elastic orthotropic medium with an arbitrarily oriented triaxial ellipsoidal inclusion is analyzed. A solution is obtained using the triple Fourier transform and the Fourier-transformed Green’s function for an infinite anisotropic medium. The high efficiency of the approach is demonstrated by solving the problem for a transversely isotropic material with a spheroidal cavity for which the exact solution is known. A numerical analysis is conducted to study the stress distribution over the surface of the inclusion with different orientations in the orthotropic space. It is revealed that in some cases the orientation of the inclusion has a strong effect on the stress concentration [ABSTRACT FROM AUTHOR]